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Journal articleNorth T, Muxworthy A, Williams W, et al., 2024,
The effect of stress on paleomagnetic signals: a micromagnetic study of magnetite's single-vortex response
, Geophysical Research Letters, Vol: 51, ISSN: 0094-8276In this study we use micromagnetic modeling to show that the magnetizations of magnetically single-vortex particles rotate toward the stress axis on the application of a differential compression stress. This is the exact opposite response to magnetically single-domain particles, which previously provided the theoretical underpinning of the effect of stress on the magnetic signals of rocks. We show that the magnetization directions of single-vortex and equant single-domain particles are altered by much lower stresses than previously predicted, c.f., 100 versus 1,000 MPa; where a change in magnetization is defined as a rotation of >3° after the removal of stress. The magnetization intensity of assemblages also drops by ∼20%–30% on the application and removal of stress of ∼100 MPa. Given that single-vortex particles are now thought to dominate the magnetization of most rocks, future studies should account for paleomagnetic directional uncertainties and potential underestimation of the ancient magnetic field intensity.
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Journal articleNagy L, Tauxe L, Williams W, et al., 2023,
Chasing tails: Insights from micromagnetic modeling for thermomagnetic recording in non-uniform magnetic structures
, Geophysical Research Letters, Vol: 49, ISSN: 0094-8276Paleointensities are key to understanding the formation and evolution of Earth and are determined from rocks which record magnetic fields upon cooling; however, experimental protocols for estimating paleointensities frequently fail. The primary reason is that laboratory protocols assume that rocks are dominated by uniformly magnetized, single-domain grains, instead of much more common non-uniformly magnetized grains. Our model for larger grains shows a multiplicity of stable domain states; with preferred states changing as a function of temperature. We show that domain state distribution depends on the thermal history of the sample—in nature and the laboratory. From numerical thermomagnetic modeling, we show that particles with non-uniform domain states will theoretically fail standard experimental paleointensity protocols, preventing us from determining reliable ancient geomagnetic field intensities. We propose that recognizing this type of behavior, and the resulting bias, will yield more reliable paleointensity records, and a better understanding of the Earth.
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Journal articleNorth TL, Collins G, Davison T, et al., 2023,
The heterogeneous response of Martian meteorite Allan Hills 84001 to planar shock
, Icarus, Vol: 390, ISSN: 0019-1035Impact-generated shock waves can change the physical properties of meteorites and their constituent minerals. Accounting for these effects is key to recovering information about the early solar system from meteorite observations. ALH 84001 is a rare ancient sample from the Martian crust, providing a unique window into the thermal and metamorphic evolution of Mars. A well-studied meteorite, past geochemical and petrologic investigations have attempted to deduce its thermal and impact history with some contradictory results. By simulating the passage of a planar shock wave through a synthetic analog for samples of ALH 84001 using the iSALE-2D shock physics code we have determined the meteorite’s likely thermodynamic and physical response during an impact. Our simulations show that heterogeneous shear heating, induced by the planar shock wave, can produce strong thermal gradients on the sub-millimeter ‘mesoscale’ throughout the meteorite, even in relatively weak shock waves (5 GPa). We are able to place new constraints on deformation events experienced by the meteorite during its time on the parent body, including the maximum pressure ALH 84001 has experienced since it acquired its remanent magnetization and its subsequent ejection from Mars.
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Journal articleRoberts AP, Zhao X, Hu P, et al., 2021,
Magnetic domain state and anisotropy in hematite (alpha-Fe2O3) from first-order reversal curve diagrams
, Journal of Geophysical Research. Solid Earth, ISSN: 2169-9356 -
Journal articleMuxworthy A, Baker E, 2021,
ThellierCoolPy: A cooling-rate correction tool for paleointensity data
, G3: Geochemistry, Geophysics, Geosystems: an electronic journal of the earth sciences, Vol: 22, Pages: 1-8, ISSN: 1525-2027We report a new approach of implementing cooling-rate corrections in absolute ancient magnetic field intensity (paleointensity) studies. Nearly all methods of determining paleointensity estimates rely on rocks having recorded a thermoremanent magnetization (TRM), on cooling from above the rock’s constituent minerals’ Curie temperature. Typically paleointensity estimates are made by comparing natural TRM, with a TRM induced in the laboratory; however, TRM intensity has long been reported to be dependent on cooling rate. Natural cooling rates are impractical in laboratories. We have developed a new cooling-rate correction method and corresponding software (ThellierCoolPy), that directly corrects the unprocessed paleointensity data, using first-order reversal curve data collected on a sister sample. This site tailored cooling-rate correction has a unique correction for each temperature step within the paleointensity data set. This new method differs from previous approaches which apply a blanket cooling-rate correction independent of the material properties of the sample. Paleointensity data from historical lavas from Parícutin, Mexico, are used to demonstrate the new software. For this data set, it is shown that cooling time of 1 million years yields a reduction of the paleointensity of ∼7%. The software is available for download.
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Journal articleHeslop D, Roberts AP, Oda H, et al., 2020,
An automatic model selection‐based machine learning framework to estimate FORC distributions
, Journal of Geophysical Research: Solid Earth, Vol: 125, Pages: 1-16, ISSN: 2169-9313First‐order reversal curve (FORC) distributions are a powerful diagnostic tool for characterizing and quantifying magnetization processes in fine magnetic particle systems. Estimation of FORC distributions requires the computation of the second‐order mixed derivative of noisy magnetic hysteresis data. This operation amplifies measurement noise, and for weakly magnetic systems, it can compromise estimation of a FORC distribution. Previous processing schemes, which are based typically on local polynomial regression, have been developed to smooth FORC data to suppress detrimental noise. Importantly, the smoothed FORC distribution needs to be consistent with the measurement data from which it was estimated. This can be a challenging task even for expert users, who must adjust subjectively parameters that define the form and extent of smoothing until a “satisfactory” FORC distribution is obtained. For nonexpert users, estimation of FORC distributions using inappropriate smoothing parameters can produce distorted results corrupted by processing artifacts, which can lead to spurious inferences concerning the magnetic system under investigation. We have developed a statistical machine learning framework based on a probabilistic model comparison to guide the estimation of FORC distributions. An intuitive approach is presented that reveals regions of a FORC distribution that may have been smoothed inappropriately. An associated metric can also be used to compare data preparation and local regression schemes to assess their suitability for processing a given FORC data set. Ultimately, our approach selects FORC smoothing parameters in a probabilistic fashion, which automates the derivative estimation process regardless of user expertise.
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Journal articleValdez Grijalva M, Nagy L, Muxworthy A, et al., 2020,
Micromagnetic simulations of first-order reversal curve (FORC) diagrams of framboidal greigite
, Geophysical Journal International, Vol: 222, Pages: 1126-1134, ISSN: 0956-540XGreigite is a sensitive environmental indicator and occurs commonly in nature as magnetostatically interacting framboids. Until now only the magnetic response of isolated non-interacting greigite particles have been modelled micromagnetically. We present here hysteresis and first-order reversal curve (FORC) simulations for framboidal greigite (Fe3S4), and compare results to those for isolated particles of a similar size. We demonstrate that these magnetostatic interactions alter significantly the framboid FORC response compared to isolated particles, which makes the magnetic response similar to that of much larger (multidomain) grains. We also demonstrate that framboidal signals plot in different regions of a FORC diagram, which facilitates differentiation between framboidal and isolated grain signals. Given that large greigite crystals are rarely observed in microscopy studies of natural samples, we suggest that identification of multidomain-like FORC signals in samples known to contain abundant greigite could be interpreted as evidence for framboidal greigite.
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Journal articleHarrison RJ, Zhao X, Hu P, et al., 2019,
Simulation of remanent, transient, and induced first-order reversal curve (FORC) diagrams for interacting particles with uniaxial, cubic, and hexagonal anisotropy
, G3: Geochemistry, Geophysics, Geosystems: an electronic journal of the earth sciences, ISSN: 1525-2027 -
Journal articleRoberts AP, Hu P, Harrison RJ, et al., 2019,
Domain state diagnosis in rock magnetism: evaluation of potential alternatives to the Day diagram
, Journal of Geophysical Research: Solid Earth, Vol: 124, Pages: 5286-5314, ISSN: 2169-9313The Day diagram is used extensively in rock magnetism for domain state diagnosis. It has been shown recently to be fundamentally ambiguous for 10 sets of reasons. This ambiguity highlights the urgency for adopting suitable alternative approaches to identify the domain state of magnetic mineral components in rock magnetic studies. We evaluate 10 potential alternative approaches here and conclude that four have value for identifying data trends, but, like the Day diagram, they are affected by use of bulk parameters that compromise domain state diagnosis in complex samples. Three approaches based on remanence curve and hysteresis loop unmixing, when supervised by independent data to avoid nonuniqueness of solutions, provide valuable component‐specific information that can be linked by inference to domain state. Three further approaches based on first‐order reversal curve diagrams provide direct domain state diagnosis with varying effectiveness. Environmentally important high‐coercivity hematite and goethite are represented with variable effectiveness in the evaluated candidate approaches. These minerals occur predominantly in noninteracting single‐domain particle assemblages in paleomagnetic contexts, so domain state diagnosis is more critical for ferrimagnetic minerals. Treating the high‐coercivity component separately following normal rock magnetic procedures allows focus on the more vexing problem of diagnosing domain state in ferrimagnetic mineral assemblages. We suggest a move away from nondiagnostic methods based on bulk parameters and adoption of approaches that provide unambiguous component‐specific domain state identification, among which various first‐order reversal curve‐based approaches provide diagnostic information.
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Journal articleNagy L, Williams W, Tauxe L, et al., 2019,
From nano to micro: evolution of magnetic domain structures in multi‐domain magnetite
, Geochemistry, Geophysics, Geosystems, Vol: 20, Pages: 2907-2918, ISSN: 1525-2027Reliability of magnetic recordings of the ancient magnetic field is strongly dependent on the magnetic mineralogy of natural samples. Theoretical estimates of long‐term stability of remanence were restricted to single‐domain (SD) states, but micromagnetic models have recently demonstrated that the so‐called single‐vortex (SV) domain structure can have even higher stability that SD grains. In larger grains ( urn:x-wiley:ggge:media:ggge21913:ggge21913-math-000110 μm in magnetite) the multidomain (MD) state dominates, so that large uniform magnetic domains are separated by narrow domain walls. In this paper we use a parallelized micromagnetic finite element model to provide resolutions of many millions of elements allowing us, for the first time, to examine the evolution of magnetic structure from a uniform state, through the SV state up to the development of the domain walls indicative of MD states. For a cuboctahedral grain of magnetite, we identify clear domain walls in grains as small as ∼3 μm with domain wall widths equal to that expected in large MD grains; we therefore put the SV to MD transition at ∼3 μm for magnetite and expect well‐defined, and stable, SV structures to be present until at least ∼1 μm when reducing the grain size. Reducing the size further shows critical dependence on the history of domain structures, particularly with SV states that transition through a so‐called “unstable zone” leading to the recently observed hard‐aligned SV states that proceed to unwind to SD yet remain hard aligned.
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Journal articlePenny C, Muxworthy A, Fabian K, 2019,
Mean-field modelling of magnetic nanoparticles: The effect of particle size and shape on the Curie temperature
, Physical review B: Condensed matter and materials physics, Vol: 99, ISSN: 1098-0121A Heisenberg mean-field model is used to study the effect of size and shape on the Curie temperature of magnetic nanoparticles. Simple cubic, body-centered cubic, and magnetite nanoparticles are modelled as spheres, cubes, and needlelike particles. The Curie temperatures of particles of different shape, but with the same crystal structure and smallest dimension d, are found to differ. The range in the value of the Curie temperature between particles of different shape, ΔTC, is found to be ∼20% of the bulk value of TC in particles where d<10 atoms. As particle size increases, the value of ΔTC reduces rapidly and becomes negligible above a threshold size. This threshold size differs between systems and is controlled predominantly by crystal structure. All systems were fit to the finite-size scaling equation, with values of the scaling exponent ν found to lie between 0.46 and 0.55, in good agreement with the expected value of ν=0.5. No trend in the value of ν due to shape was found.
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Journal articleKu J, Valdez-Grijalva M, Deng R, et al., 2019,
Modelling external magnetic fields of magnetite particles: From micro- to macro-scale
, Geosciences, Vol: 9, ISSN: 2076-3263We determine the role of particle shape in the type of magnetic extraction processes used in mining. We use a micromagnetic finite element method (FEM) to analyze the effect of external magnetic fields on the magnetic structures of sub-micron magnetite particles. In non-saturating fields, the magnetite particles contain multiple possible non-uniform magnetization states. The non-uniformity was found to gradually disappear with increasing applied field strength; at 100 mT the domain structure became near uniform; at 300 mT the magnetic structure saturates and the magnetization direction aligned with the field. In magnetic separation techniques, we suggest that 100 mT is the optimal field for magnetite to maximize the magnetic field with the lowest energy transfer; larger particles, i.e., >1 µm, will likely saturate in smaller fields than this. We also examined the effect of external magnetic fields on a much larger irregular particle (L × W × H = 179.5 × 113 × 103 μm) that was too large to be examined using micromagnetics. To do this we used COMSOL. The results show the relative difference between the magnitude of magnetic flux density of the particle and that of a corresponding sphere of the same volume is <5% when the distance to the particle geometry center is more than five times the sphere radius. The ideas developed in this paper have the potential to improve magnetic mineral extraction yield.
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Journal articleShah J, Williams W, Almeida TP, et al., 2018,
The oldest magnetic record in our solar system identified using nanometric imaging and numerical modeling
, Nature Communications, Vol: 9, ISSN: 2041-1723Recordings of magnetic fields, thought to be crucial to our Solar System’s rapid accretion, are potentially retained in unaltered nanometric low-Ni kamacite (~metallic Fe) grains encased within dusty olivine crystals, found in the chondrules of unequilibrated chondrites. However, most of these kamacite grains are magnetically non-uniform, so their ability to retain four-billion-year-old magnetic recordings cannot be estimated by previous theories, which assume only uniform magnetization. Here, we demonstrate that non-uniformly magnetized nanometric kamacite grains are stable over Solar System timescales and likely the primary carrier of remanence in dusty olivine. By performing in-situ temperature-dependent nanometric magnetic measurements using off-axis electron holography, we demonstrate the thermal stability of multi-vortex kamacite grains from the chondritic Bishunpur meteorite. Combined with numerical micromagnetic modeling, we determine the stability of the magnetization of these grains. Our study shows that dusty olivine kamacite grains are capable of retaining magnetic recordings from the accreting Solar System.
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Journal articleDavison TM, Derrick JG, Collins GS, et al., 2017,
Impact-induced compaction of primitive solar system solids: The need for mesoscale modelling and experiments
, Procedia Engineering, Vol: 204, Pages: 405-412, ISSN: 1877-7058Primitive solar system solids were accreted as highly porous bimodal mixtures of mm-sized chondrules and sub-μm matrix grains. To understand the compaction and lithification of these materials by shock, it is necessary to investigate the process at the mesoscale; i.e., the scale of individual chondrules. Here we document simulations of hypervelocity compaction of primitive materials using the iSALE shock physics model. We compare the numerical methods employed here with shock compaction experiments involving bimodal mixtures of glass beads and silica powder and find good agreement in bulk material response between the experiments and models. The heterogeneous response to shock of bimodal porous mixtures with a composition more appropriate for primitive solids was subsequently investigated: strong temperature dichotomies between the chondrules and matrix were observed (non-porous chondrules remained largely cold, while the porous matrix saw temperature increases of 100’s K). Matrix compaction was heterogeneous, and post-shock porosity was found to be lower on the lee-side of chondrules. The strain in the matrix was shown to be higher near the chondrule rims, in agreement with observations from meteorites. Chondrule flattening in the direction of the shock increases with increasing impact velocity, with flattened chondrules oriented with their semi-minor axis parallel to the shock direction.
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Journal articleNagy L, Williams W, Muxworthy AR, et al., 2017,
Stability of equidimensional pseudo-single domain magnetite over billion year time-scales
, Proceedings of the National Academy of Sciences of the United States of America, Vol: 114, Pages: 10356-10360, ISSN: 1091-6490Interpretations of paleomagnetic observations assume that naturally occurring magnetic particles can retain their primary magnetic recording over billions of years. The ability to retain a magnetic recording is inferred from laboratory measurements, where heating causes demagnetization on the order of seconds. The theoretical basis for this inference comes from previous models that assume only the existence of small, uniformly magnetized particles, whereas the carriers of paleomagnetic signals in rocks are usually larger, nonuniformly magnetized particles, for which there is no empirically complete, thermally activated model. This study has developed a thermally activated numerical micromagnetic model that can quantitatively determine the energy barriers between stable states in nonuniform magnetic particles on geological timescales. We examine in detail the thermal stability characteristics of equidimensional cuboctahedral magnetite and find that, contrary to previously published theories, such nonuniformly magnetized particles provide greater magnetic stability than their uniformly magnetized counterparts. Hence, nonuniformly magnetized grains, which are commonly the main remanence carrier in meteorites and rocks, can record and retain high-fidelity magnetic recordings over billions of years.
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Journal articleWatters WA, Hundal CB, Radford A, et al., 2017,
Dependence of secondary crater characteristics on downrange distance: high-resolution morphometry and simulations
, Journal of Geophysical Research: Planets, Vol: 122, Pages: 1773-1800, ISSN: 2169-9097On average, secondary impact craters are expected to deepen and become more symmetric as impact velocity (vi) increases with downrange distance (L). We have used high-resolution topography (1–2 m/pixel) to characterize the morphometry of secondary craters as a function of L for several well-preserved primary craters on Mars. The secondaries in this study (N = 2644) span a range of diameters (25 m ≤D≤400 m) and estimated impact velocities (0.4 km/s ≤vi≤2 km/s). The range of diameter-normalized rim-to-floor depth (d/D) broadens and reaches a ceiling of d/D≈0.22 at L≈280 km (vi= 1–1.2 km/s), whereas average rim height shows little dependence on vi for the largest craters (h/D≈0.02, D > 60 m). Populations of secondaries that express the following morphometric asymmetries are confined to regions of differing radial extent: planform elongations (L< 110–160 km), taller downrange rims (L < 280 km), and cavities that are deeper uprange (L< 450–500 km). Populations of secondaries with lopsided ejecta were found to extend to at least L ∼ 700 km. Impact hydrocode simulations with iSALE-2D for strong, intact projectile and target materials predict a ceiling for d/D versus L whose trend is consistent with our measurements. This study illuminates the morphometric transition from subsonic to hypervelocity cratering and describes the initial state of secondary crater populations. This has applications to understanding the chronology of planetary surfaces and the long-term evolution of small crater populations.
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Journal articleShah J, Bates H, Muxworthy AR, et al., 2017,
Long-lived magnetism in chondrite parent bodies
, Earth and Planetary Science Letters, Vol: 475, Pages: 106-118, ISSN: 1385-013XWe present evidence for both early- and late-stage magnetic activity on the CV and L/LL parent bodies respectively from chondrules in Vigarano and Bjurböle. Using micro-CT scans to re-orientate chondrules to their in-situ positions, we present a new micron-scale protocol for the paleomagnetic conglomerate test. The paleomagnetic conglomerate test determines at 95% confidence, whether clasts within a conglomerate were magnetized before or after agglomeration, i.e., for a chondritic meteorite whether the chondrules carry a pre- or post-accretionary remanent magnetization. We found both meteorites passed the conglomerate test, i.e., the chondrules had randomly orientated magnetizations. Vigarano's heterogeneous magnetization is likely of shock origin, due to the 10 to 20 GPa impacts that brecciated its precursor material on the parent body and transported it to re-accrete as the Vigarano breccia. The magnetization was likely acquired during the break-up of the original body, indicating a CV parent body dynamo was active ∼9 Ma after Solar System formation. Bjurböle's magnetization is due to tetrataenite, which transformed from taenite as the parent body cooled to below 320 °C, when an ambient magnetic field imparted a remanence. We argue either the high intrinsic anisotropy of tetrataenite or brecciation on the parent body manifests as a randomly orientated distribution, and a L/LL parent body dynamo must have been active at least 80 to 140 Ma after peak metamorphism. Primitive chondrites did not originate from entirely primitive, never molten and/or differentiated parent bodies. Primitive chondrite parent bodies consisted of a differentiated interior sustaining a long-lived magnetic dynamo, encrusted by a layer of incrementally accreted primitive meteoritic material. The different ages of carbonaceous and ordinary chondrite parent bodies might indicate a general difference between carbonaceous and ordinary chondrite parent bodies, and/or format
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Journal articleMuxworthy AR, Bland PA, Davison TM, et al., 2017,
Evidence for an impact-induced magnetic fabric in Allende, and exogenous alternatives to the core dynamo theory for Allende magnetization
, Meteoritics & Planetary Science, Vol: 52, Pages: 2132-2146, ISSN: 1086-9379We conducted a paleomagnetic study of the matrix of Allende CV3 chondritic meteorite, isolating the matrix’s primary remanent magnetization, measuring its magnetic fabric and estimating the ancient magnetic field intensity. A strong planar magnetic fabric was identified; the remanent magnetization of the matrix was aligned within this plane, suggesting a mechanism relating the magnetic fabric and remanence. The intensity of the matrix’s remanent magnetization was found to be consistent and low (~6 μT). The primary magnetic mineral was found to be pyrrhotite. Given the thermal history of Allende, we conclude that the remanent magnetization formed during or after an impact event. Recent mesoscale impact mode ling, where chondrules and matrix are resolved, has shown that low-velocity collisions can generate significant matrix temperatures, as pore-space compaction attenuates shock energy and dramatically increases the amount of heating. Non-porous chondrules are unaffected, and act as heat-sinks, so matrix temperature excursions are brief. We extend this work to model Allende, and show that a 1km/s planar impact generates bulk porosity, matrix porosity, and fabric in our target that match the observed values. Bimodal mixtures of a highly porous matrix and nominally zero-porosity chondrules, make chondrites uniquely capable of recording transient or unstable fields. Targets that have uniform porosity, e.g., terrestrial impact craters, will not record transient or unstable fields. Rather than a core dynamo, it is therefore possible that the origin of the magnetic field in Allende was the impact itself, or a nebula field recorded during transient impact heating.
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Journal articleJourdan F, Timms NE, Eroglu E, et al., 2017,
Collisional history of asteroid Itokawa
, Geology, Vol: 45, Pages: 819-822, ISSN: 1943-2682In situ extrate rrestrial samples returned for study (e.g., from the Moon) are crucial in understanding the origin and evolution of the Solar System as, contrary to meteorites, they provide a known geological context for the samples and their analyses. Asteroid 25143 Itokawa is a rubble pile asteroid consisting of reaccumulated fragments from a catastrophically disrupted monolithic parent asteroid, and from which regolith dust particles have been recovered by the Hayabusa space probe. We analyzed two dust particles using Electron Backscatter Diffraction (EBSD) and 40 Ar/39 Ar dating techniques. One of the grains showing signs of 15–25 GPa impact shock pressure, yielded a 40 Ar/Ar plateau age of 2.3 ± 0.1 Ga. We develop a novel temperature -pressure-porosity model, coupled with diffusion models to show that the relatively low pressure and high temperature involved in the impact process can be reconciled only if the asteroid was already made of porous material at ~2.3 Ga and thus, if asteroid Itokawa was already formed, thereby providing a minimum age for catastrophic asteroid breakup. A second particle shows no sign of deformation indicating shock pressure of ˂ 10 GPa and a calculated maximum temperature of ~200 °C. This low temperature estimate is compatible with a lack of isotopic resetting for this particle. This suggests that the breakup of Itokawa’s parent was a relatively low-temperature process at the scale of the asteroid, and occurred on a pre-shattered parent body.
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Journal articleBerndt T, Paterson GA, Cao C, et al., 2017,
Experimental test of the heating and cooling rate effect on blocking temperatures
, Geophysical Journal International, Vol: 210, Pages: 255-269, ISSN: 1365-246XThe cooling rates at which rocks acquire thermoremanent magnetizations (TRMs), affect their unblocking temperatures in thermal demagnetization experiments; similarly the heating rates at which the thermal demagnetization experiments are done also affect the unblocking temperature. We have tested the effects of variable cooling and heating rates on the unblocking temperatures of two natural non-interacting, magnetically uniform (single-domain, SD) (titano)magnetite samples and a synthetic SD magnetoferritin sample. While previous studies have only considered unblocking temperatures for stepwise thermal demagnetization data (i.e. the room-temperature magnetization after incremental heating), in this work we derive an expression for continuous thermal demagnetization of both TRMs and viscous remanent magnetizations (VRMs) and relate the heating rate to an effective equivalent hold time of a stepwise thermal demagnetization experiment. Through our analysis we reach four main conclusions: First, the theoretical expressions for the heating/cooling rate effect do not accurately predict experimentally observed blocking temperatures. Empirically, the relation can be modified incorporating a factor that amplifies both the temperature and the heating rate dependence of the heating/cooling rate effect. Using these correction factors, Pullaiah nomograms can accurately predict blocking temperatures of both TRMs and VRMs for continuous heating/cooling. Second, demagnetization temperatures are approximately predicted by published ‘Pullaiah nomograms’, but blocking occurs gradually over temperature intervals of 5–40 K. Third, the theoretically predicted temperatures correspond to ∼54–82 per cent blocking, depending on the sample. Fourth, the blocking temperatures can be used to obtain estimates of the atomic attempt time τ0, which were found to be 3 × 10−10 s for large grained (titano)magnetite, 1 × 10−13&t
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